Indentation on a one-dimensional hexagonal quasi-crystal half-space by an elliptic indenter

Abstract

We investigate the contact between a one-dimensional (1D) hexagonal quasi-crystal (QC) half-space and a rigid elliptic indenter. The three-dimensional (3D) phonon–phason fields in the half-space are derived in terms of elementary functions using the generalized potential theory method. Closed-form solutions are obtained for significant physical quantities, including the contact stresses, indentation forces, contact stiffness and stress intensity factor (SIF). Numerical calculations are performed to validate the analytical solutions and to show the distributions of the coupled 3D fields. The effects of indentation depths, contact region geometry, indenter size and phason field on the indentation forces, contact stiffness and SIFs are also delineated. The analytical solutions can serve as a theoretical basis for further studying elasto-plastic and adhesive contacts on QCs.